# Learn about What is The Difference Between a Parameter and a Statistic?

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Last Updated on February 21, 2023 by Tabraiz

## What are statistics?

It is a value determined by sampling and has a numeric value. A statistician obtains data from various sources randomly selected from a group. So, this data is utilized to determine the overall value of the issue or problem using descriptive statistical measures. The data is measured using formulas and a value is determined. From an entire population, they choose a particular group or some items, objects, people, etc. So, by studying the behavior or pattern of the samples obtained, they conclude the characteristics or value of the population. The main objective of statistic is to estimate or determine a particular parameter.

A statistician can also obtain several samples from a population. They can obtain results from different samples that are variant.

## What is a parameter?

A statistician, after determining the values of all the samples, concludes the characteristics or value of a population. So, a parameter is the characteristic or value determined based on all the elements or sample. It is also considered an aggregate of the overall units after considering certain characteristics. The numeric value determined after calculating the aggregate of the samples remains unchanged. So, to know the parameters, every member of the population is determined. The value determined after determining the aggregate is the true value. It is obtained after a census is conducted.

## Know what is the difference between parameters and statistics?

Now ,we will study about the what is the difference between a parameter and a statistic? and their differences are highlighted below.

A statistic is also a sample and is obtained from a small portion of the population. The statistician concludes after examining a small portion of the entire population. But a parameter is a value or a characteristic obtained from aggregate samples.

A statistic has a certain value or a number that is derived from a sample of the population. This parameter has no specific numeric value. It is described in terms of its characteristics.

The notations specified for different population parameters are different, and the sample statistics are as under:

For population parameters, mu means mean. Population parameters are determined by P. Sigma is also represented by the standard deviation. N means the size of the population; the standardized variety is also represented by z. The coefficient of variation is labelled with a symbol.

In the world of sample statistics, standard deviation is represented by the symbol s, x-bar means mean, and variance is stated with s power. Standard or error means sp and a standardized variety is labelled as x-x. The coefficient is denoted by the symbol (x).

## Some of the common parameters

Central tendency is one of the most used parameters. It includes different values of mean, mode, and median. It implies the behavior of the data in a distribution.

### Median

It is a factor used for calculating variables and is measured with ratio scales or ordinal intervals. Initially, the data is assembled from the lowest value to the highest value, and then a number is picked in between. Then, the middle number is chosen. If the total value of the data points is an odd number, then it is considered a middle number. If the number determined is even, then the median should be added by choosing two middle numbers. It should be divided by 2 to determine the mean.

### Mean

The mean is known as the average and is used commonly. It is used among the three measures of central tendency. This parameter is also used to describe the distribution of ratios.

### Mode

It is a numeric value commonly occurring in a data distribution. It determines the highest value or the highest number in a dataset or it shows the most common number in the dataset.

## How do you estimate parameters from statistics?

You can calculate the population parameter using the method of inferential statistics for sample statistics. The value that is obtained should be accurate, and hence you should present a sample that actually represents your population, even if randomly selected.

The two types of estimates determined are interval estimates and point estimates.

The interval estimates provide a range of values to represent the parameter. A point estimate is a specific or single value of a parameter. It is based on statistical sampling. A sample mean is the point estimate of a population mean.

To clearly obtain data, both types of estimates are used.

## Statistics and parameters

A parameter is a factor that determines the whole population. For instance, if you want to know the length of a butterfly, we label it a parameter because it specifically states the length value or a portion of a butterfly.

You cannot easily determine a parameter as we should know the corresponding statistical value to calculate the value. Statistics refers to a sample drawn from a larger population, and it describes only a subset of that population. The parameter is the aggregate of all the samples. As an example, we cannot catch several butterflies instantly, but we can catch only 100 butterflies. We can measure the length of 100 butterflies and simply conclude the aggregate length of the butterflies. So, we can say that the length of the butterfly is approximately xxx.

The value of the sample varies, but the parameter is fixed. If we determine the overall length of 100 butterflies is 6.5, but the value of another 100 butterflies can be 6.8.

The overall length of 50 butterflies is 7.0 mm. So, from the sample of 50 butterflies, a statistician may conclude that the length of the butterflies is 7.0mm.

## Parameters vs. Statistics

Researchers are keen to understand the concept of population parameters. Even if you understand the value of the parameters, you cannot obtain the information comprehensively. Scientists usually do not focus on sampling or the value obtained from the sample. They want to understand the mean effect of the entire population.

Determining parameters by examining the whole population is sometimes impossible as the population is too large. Inferential statistics should use sample statistics to determine the value of a population.

So, to determine a value or parameter, they should use a sampling method to produce various samples. So, scientists are using the methods of random sampling, and then the analysts are using the method of statistical analysis to know the errors obtained from sampling. So, the population parameter is then obtainedSo this what is the difference between parameters and statistics.